1. ## Hyperbola

I can determine a hyperbola in this equations, like finding the foci, axes, vertecis, intercepts?

x^2+y2=100 <--- is a circle
xy=48

2. As you have pointed out, the first equation is a circle. The second happens to be a hyperbola.

To make life easier $xy = 48 \implies y = \frac{48}{x}$

This should make life easier for finding the charateristics you describe above.

3. how can i write this $y= \frac{48}{x}$ into this equation $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ of hyperbola?

I graphed this y=48/x

it turns like this:

http://www.flickr.com/photos/49966448@N07/4587282411/

but i dont know how to get the foci, axes, vertices, etc.